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On the Einstein Relation for Hopping Electrons
Author(s) -
Baranovskii S. D.,
Faber T.,
Hensel F.,
Thomas P.
Publication year - 1998
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/(sici)1521-3951(199801)205:1<87::aid-pssb87>3.0.co;2-p
Subject(s) - einstein relation , variable range hopping , condensed matter physics , diffusion , monte carlo method , physics , electron , relaxation (psychology) , exponential function , statistical physics , semiconductor , materials science , electrical resistivity and conductivity , quantum mechanics , mathematics , statistics , psychology , social psychology , mathematical analysis , operations management , economics , metric (unit)
Diffusion coefficient of carriers, D , and their mobility, μ, in disordered semiconductors at very low temperatures are temperature‐independent, being determined by the energy‐loss hopping of carriers through localized band‐tail states. In such a hopping relaxation in a system with exponential density of tail states, the relation between μ and D has the form μ ∼ eD /ε 0 , where ε 0 is the energy scale of the exponential band tail. With rising temperature, thermally‐activated hopping transitions increase their contribution to transport processes and the model of the energy‐loss hopping is not applicable. We study by a Monte Carlo computer simulation how the relation between μ and D evolves with increasing temperature from its temperature‐independent form at T = 0 to the conventional Einstein relation μ = eD / kT .